Quantum phase transition in a two-dimensional quantum Ising model: Tensor network states and ground-state fidelity

Abstract

The purpose of this paper is to describe how to describe the phase transition of quantum multibody system from the perspective of the basic concept of quantum information science - fidelity. For systems the traditional way of characterization that undergo a quantum phase transition is Landau's introduction of order and the fluctuation. In particular, for phase transitions caused by spontaneous breaking symmetry, that is, different ground state wave functions are orthogonal to each other. This suggests that, contrary to the ups and downs of traditional expressions, the concept of irrelevant information and vital information can be introduced. By introducing the basic amount of ground lattice fidelity, quantifying irrelevant information and critical information which can identify the quantum phase transition of the system. It is worth emphasizing that no matter the internal order of quantum multibody systems is a traditional symmetry or other novel quantum order, they all can be applied such as topological order, single-grid ground state fidelity. In order to efficiently calculate the single-grid ground state fidelity of quantum multibody systems, tensor network algorithm is needed. This kind of algorithm is the result of the deepening of quantum entanglement in recent years. Quantum entanglement expounds the working principle of real-space renormalization group algorithm, especially density matrix re-grouping algorithm.